Hey oldschool, I also have a BHK 250 and BHK pre like you do. When used together, they are extremely quiet. But when I used the BHK 250 with other pre amps and DAC’s I sometimes got a little noise. Using the XLR connection when I could eliminated that. My BHK 250 was always dead quiet with XLR.
Also, try a different set of tubes. Even if the tubes are new, they can be bad. It might not even be both tubes, just one tube humming but you can’t tell. So if you have another set of tubes to throw in, give it a shot. And try tube dampers if you can. I have tube dampers (little silicone rings) and they made a small improvement on the tubes in my BHK pre.
And just a few basic things, but like another poster suggested, try a cheater plug. And make sure the little panel that covers the tubes is screwed down tightly. If that metal panel is a little loose, that can be contributing to the hum... And although this last suggestion isn’t very practical, if you can bring the amp to another location, ie friends house or workplace, plug it in there and see if there’s still a hum. The BHK 250 is a little heavy though and not something you wanna carry around town.
I’m not saying that dirty power isn’t causing the humming but I’m just suggesting things you can do before you go down the rabbit hole of power conditioning and noise blockers. Good luck.